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Current Electricity
Current Current is the flow of charge per unit time through a cross sectional area . I = Q/t I = neAVd Current and charge remain the same in series . Voltafe is lost so that current remains the same . Potential Difference THe work done in moving a test positive charge from one point to another in an electric field is calld as Potential Difference . V = W / Q Voltage remains same in parallel combination . The current gets distributed according to voltages in the parallel branches . Ohm's Law The Ohm's law states that the current flowing through a metallic conductor is directly proportional to the potential difference across its terminals provided that the physical factors remain constant . V = RI Resistance and Resistivity The tendency to oppose the flow of current is called as Resistance . The resistance of a wire of unit length and unit area of cross section is called Resistivity . Resistivity is the fundamental property of a material . The resistance can be changed by modifying the length and Area of cross section . Resistivity remains constant . Resistivity can change only if temperature is changed considerably . When a 50 ohm wire is divided into 5 equal parts , the resistance of each part is 10 ohm . Drift Velocity J = nev v = J/ne I = neAVd NOTE : Current flows in opposite direction of drift velocity . Temperature Dependence of Resistance The temperature coefficient of resistance is defined as the rise in resistance per unit rise in temperature per unit original length . PTC and NTC If Resistance/Resistivity increases with increase in temperature (positive slope) , it is PTC (Positive Temperature Co-efficient) e.g. Metals , Conductors . If Resistance decreases with increase in temperature (negative slope) , it is NTC (Negative Temperature co-efficient) e.g. Semiconductors Note : The resistivity changes with temprature , thus changing the resistance . Thermistor They are also called Thermal Resistors . Resistances which are affected by temperature . Two types NTC , PTC . Thermisters are made up of metal oxides of high co-efficient of resistivity . Thermal Effect of Current When we have a thermo-couple , one at hot end and other being cold , the variation in EMF is given as :- e = aθ + bθ2 The temperature at which the EMF is maximum is called as Neutral Temperature '. At the '''inversion temperature ', the polarity of the emf is reversed . The graph of variation of emf starts from cold junction and goes maximum up to neutral temperature and then starts decreasing as we move towards hot junction . θn = (θi + θc ) / 2 Colour Code for Resistors B B R O Y G B V G W G S N Combination of Resistors Series Rs = R1 + R2 +... + Rn Parallel 1/Rp = 1/R1 + 1/R2 + ...... + 1/Rn Combination of Cells Series The Voltages are added to give effective voltage . Parallel The voltages remain same throughout the combination . Electro Motive Force The force provided by voltage source , so as to overcome the resistance of the conductor is called as Electromotive Force . For ideal Battery , E = V For a cell with internal resistance r , V = E - ir . NOTE : For EMF, Internal Resistance has to be considered as well . Internal Resistance If the internal resistance of a cell is zero , then it will supply constant current to the circuit . Work Done by Electric Work done = I2Rt 1 eV is the amount of electric work done when a single electron flows through the conductor when 1 volt of P.D. is applied across its terminals . 1eV = 1.6 x10-19 J Heating Effect of Electric Current H = I2Rt = V2/R = VIt Electric Power Electric power is the rate of doing work . It can also be defined as the rate at which electric energy is consumed . P = I2R = V2/Rt = VI Kirchoff's Laws '''Kirchoff's Current Law It states that the sum of current at a junction is zero . The current flowing towards the junction is taken as positive and the current flowing away from the junction is taken as negative . Kirchoff's Voltage Law It states that the sum of EMFs and Voltages (IR) in a loop is equal to zero . EMFs in the direction of the loop is taken as positive , while against the loop is taken as negative . Voltages (IR) in the direction is loop is taken as negative and against the loop is taken as positive . Note : For MCQs , whenever there are a large number of voltages , EMFs or currents , use Kirchoof's Loop Laws Wheatstone's Network The Wheatstone's Network consists of four resistances through which a galvanometer is connected . The unknown resistance can be calculated by the formula R1 / R2 = R3 / R4 , . i.e. Left/ Right = Left / Right . Note : The middle resistance is ignored when the network is balanced . Wheatstone's Meterbridge Wheatstone's Meterbridge and potentiometer work on the principle of Wheatstone,s Network . Wheatstone's meterbridge consists of two L shaped wooden strips , between which , two resistors are connected . A Jockey , containing a centre - zero deflection galvanometer is connected at a point between the two resistors . A 1 m long wire is connected below the resistors . The switch is turned on and the jockey is now tapped at point A . It is then tapped at point C . It should give deflections on either sides , if not adjust the rheostat . Now , start tapping the wire till you reach a point , where the deflection is zero . Take this distance as l . hence , the remaining distance is (100 - l) cm . The wire AC has certain resistance , which is directly proportional to the length of the wire . Using this relation we can find the unknown resistance connected above on one of the wooden planks . The relation in Wheatstone's Meterbridge is :- R1 / R2 = R3 / R4 Post Office Box Kelvin's Method Potentiometer A potentiometer is like an ideal voltmeter , because it does not draw any current from the circuit . Principle V α l ... Potential Gradient = Constant A) Comparison Method E1 / E2 = l1 / l2 B) Combination Method E1 + E2 / E1 - E2 = L1 / L2 C) Internal Resistance r = R - l2) / l2 Capacitors in Circuit While in steady state , no current flows through capacitor . Capacitors in Series 1/Cp = 1/C1 + 1/C2 + ...... + 1/Cn Capacitors in Parallel Cs = C1 + C2 +... + Cn Charging and Discharging of Capacitors THe graph of charge v/s time of Capaitor is exponential . Charging : ''' q = EC(1 - e-t/CR) '''Discharging : q = Qe-t/CR Tips & Tricks # When n resistors of Resistance R are connected in series , the total resistance is nR . # When n series of Resistance R are connected in parallel , the total resistance is R/n . # If a wire of resistance R is stretched n (l2/l1) times , The new resistance is n2R # When a complicated symmetric circuit is given for finding resistance , it can be divided into halves to simplify the circuit . # When simplifying a circuit , plot points on the circuit to guide you . # In Wheatstone's network , if the network is balanced , the middle resistance is ignored because no current flows through it . # Whenever , a part of circuit confuses you , remove it and see it's role in the circuit . # The effective resistance for a balanced Wheatstone's Network is R # For equivalent resistances , consider current through each branch . # Use Kirchoff's laws for complicated circuits . Category:Physics